Subgroups — C₄⋊#20294111 #42122938

Order 27712.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20294111	C₂	1	2	yes	maximal
2	C₄×#16812367	C₂	1	1	yes	maximal, characteristic
3	#20294111	—	2	2	no	—
4	C₂×#16812367	C₄	1	1	yes	characteristic
5	C₂×#16812367	C₂²	1	1	yes	characteristic
6	C₄×#13181884	C₄	1	1	yes	characteristic
7	#16812367	—	2	1	no	—
8	#16812367	D₄	1	1	yes	characteristic
9	#16812367	Q₈	1	1	yes	characteristic
10	C₂×#13181884	C₈	1	1	yes	characteristic
11	C₂×#13181884	C₂×C₄	1	1	yes	characteristic
12	C₄×D₄₃₃	C₈	1	1	yes	characteristic
13	C₂×D₄₃₃	C₂×C₈	1	1	yes	characteristic
14	#13181884	—	2	1	no	—
15	#13181884	C₄⋊C₄	1	1	yes	characteristic
16	#13181884	M₁₆	1	1	yes	characteristic
17	C₄×C₄₃₃	C₁₆	1	1	yes	characteristic, complemented
18	Dic₄₃₃	C₁₆	1	1	yes	characteristic, complemented
19	C₂×C₄₃₃	C₂×C₁₆	1	1	yes	characteristic
20	D₄₃₃	C₄⋊C₈	1	1	yes	characteristic
21	D₄₃₃	M₃₂	1	1	yes	characteristic
22	C₄₃₃	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
23	C₄⋊C₁₆	—	433	1	no	maximal, Sylow
24	C₂×C₁₆	—	433	2	no	—
25	C₄×C₈	—	433	1	no	—
26	C₂×C₈	—	433	1	no	—
27	C₂×C₈	—	433	1	no	—
28	C₄²	—	433	1	no	—
29	C₁₆	—	866	2	no	—
30	C₂×C₄	—	433	1	no	—
31	C₂×C₄	—	433	1	no	—
32	C₂×C₄	—	433	1	no	—
33	C₈	—	866	1	no	—
34	C₈	—	433	1	no	—
35	C₈	—	433	1	no	—
36	C₂²	—	433	1	no	—
37	C₄	—	866	1	no	—
38	C₄	—	433	1	no	—
39	C₄	—	433	1	no	—
40	C₄	—	433	1	no	—
41	C₄	#20294111	1	1	yes	characteristic, complemented
42	C₂	—	433	1	no	—
43	C₂	—	433	1	no	—
44	C₂	C₂×#20294111	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.